{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "mu, sigma = 0, 0.4 # mean and standard deviation\n",
    "x = np.random.normal(mu, sigma, 100000)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c478910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "count, bins, ignored = plt.hist(x, 500, norm=True)\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('p(x)')\n",
    "plt.title('Histogram of IQ')\n",
    "plt.text(60, .025, r'$\\mu=100,\\ \\sigma=15$')\n",
    "plt.axis([40, 160, 0, 0.03])\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "plt.show()\n",
    "#prob_x = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) );\n",
    "    \n",
    "#plt.plot(bins, prob_y, linewidth=2, color='b')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TbT2/5OfNRabeUmTmKAOZ+vKQqQMAKOptw2UzqsDzqjmIX1omawIvYFbpufd5LS8O8QsA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\nb8xdjTFssAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b3b7190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_y = np.array(x);\n",
    "for i in range(0,len(x)):\n",
    "    prob_y[i] = np.arctan(x[i])\n",
    "    \n",
    "#prob_y = np.arctan(x)\n",
    "plt.hist(prob_y, 5000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dr3/t1WAlpZTwY1u5Ek47zbct7NNHsxYkv5xySsXm5wMG+KpySRlNy4xpwwY4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\n5AklfBGRPPH/AWUeEe+Fym9IAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109371650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "mu, sigma = 0, 0.4 # mean and standard deviation\n",
    "x = np.random.normal(mu, sigma, 100000)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
